Maths

• Integers


  Whole numbers, either positive or negative
• Integers


  • -385, 0, 1, 17, 989, 1234567890
• Non-integers


  • 0.5, 2.7, 13.1000.1, 68.88
• Square numbers


  A number multiplied by itself
• Cube numbers


  A number multiplied by itself, then by itself again
• BODMAS


  Order of operations: Brackets, Other (powers/roots), Division, Multiplication, Addition, Subtraction
• To find the reciprocal of a number, take the square root, then subtract 10, then take the square root again, and finally take the reciprocal
• Multiplying/dividing by 10, 100, 1000 etc. involves moving the decimal point
• Multiplying/dividing whole numbers uses traditional methods like long multiplication and short division
• Multiplying/dividing decimals involves counting decimal places and aligning the decimal point in the answer
• Dividing a number by a decimal is the same as dividing by the decimal's reciprocal
• Multiplying Decimals


  1. Start by ignoring the decimal points. Do the multiplication using whole numbers
  2. Count the total number of digits after the decimal points in the original numbers. Make the answer have the same number of decimal places
• Dividing a Decimal by a Whole Number


  Set the question out like a whole-number division, just put the decimal point in the answer right above the one in the question
• Dividing a Number by a Decimal


  This works if you're dividing a whole number by a decimal, or a decimal by a decimal
• Dividing a Decimal by a Decimal


  1. Write it as a fraction
  2. Get rid of the decimals by multiplying top and bottom by 100
  3. It's now a decimal-free division that you know how to solve
• Negative Numbers


  Numbers less than zero
• Example 1


  • Rachel is making cupcakes. Each cupcake needs 1/4 of a pack of butter. How many packs of butter will Rachel need to buy to make 30 cupcakes?
• Adding and Subtracting with Negative Numbers


  Use the number line, move left to subtract, move right to add
• Solving Example 1


  1. 1 cupcake needs 1/4 of a pack of butter

  2. 30 cupcakes need 30 x 1/4 = 7.5 packs of butter

  3. Convert to a whole number of packs (round up)

  4. Rachel will need to buy 8 packs of butter
• The temperature in Mathchester was 4°C on Monday, -2°C on Tuesday, and 3°C lower than Tuesday on Wednesday
• Example 2


  • The diamond is made up of two identical equilateral triangles. The top triangle is split into three equal triangles. The bottom triangle is split into two equal triangles. Find the fraction of the diamond that is shaded.
• Prime Numbers


  Numbers that only divide by 1 and themselves
• Solving Example 2


  1. 1/3 of the top triangle is shaded

  2. 1/2 of the bottom triangle is shaded

  3. Find a common denominator to add the fractions

  4. The shaded fraction is 5/6 of the diamond
• 1 is not a prime number, 2 is the only even prime number</b>
• Prime numbers end in 1, 3, 7 or 9 (except 2 and 5)
• Example 3


  • Which of the fractions 11/13 or 8/9 is closer to 1?
• Finding Prime Numbers


  Get rid of numbers not ending in 1, 3, 7 or 9

  1. Divide the remaining numbers by 3 and 7, keep the ones that don't divide exactly
• Solving Example 3


  1. Convert the fractions to a common denominator

  2. 11/13 = 33/39, 8/9 = 36/39

  3. Subtract each fraction from 1 to see which is closer
• 2 is the only even prime number
• Fractions, decimals and percentages are different ways of representing the same thing
• Prime numbers in the list

  • 4, 6, 10, 14, 15, 17
• You should learn the common conversions between them
• Recurring Decimals


  Decimals with a repeating pattern of digits
• LCM (Lowest Common Multiple)


  The smallest number that is a multiple of all the given numbers
• Converting Recurring Decimals


  1. Identify the repeating pattern

  2. Mark the repeating digits with dots

  3. Convert to a fraction
• HCF (Highest Common Factor)

  The largest number that divides all the given numbers
• Numbers


  • 4
  • 6
  • 10
  • 14
  • 15
  • 17
  • 24
  • 301
• Example 4


  • Year 10 is split into two classes, each with the same number of pupils. 1/4 of one class are girls, and 3/8 of the other class are girls. What fraction of year 10 students are girls?
• Solving Example 4


  1. Divide each fraction by 2 to find the number of girls in each class as a fraction of total year 10 pupils

  2. Add the fractions to find the total fraction of year 10 pupils that are girls
• Multiple of 2, multiple of 3, multiple of 4


  • One number that satisfies these criteria